This document presents the Pythagorean theorem. The theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. It proves this theorem by showing that two triangles formed from a right triangle are similar, allowing relationships between the sides to be determined and combined to derive the theorem.

1. THIS IS RIGHT ANGLED TRIANGLE HAVING ONE OF ITS SIDES A RIGHT ANGLE
Come on lets learn ‘PYTHGOREAN THEOREM’
푎2 + 푏2 = 푐2
90

2. PYTHOGOREAN THEOREM STATEMENT
IN A RIGHT ANGLED TRIANGLE,THE SQUARE OF THE HYPOTENUSE IS EQUAL TO THE
SUM OF THE SQUARES ON THE OTHER TWO SIDES

3. THE THING WHICH SHOULD BE KNOWN TO LEARN THE THEOREM IS:
• HYPOTENUSE : Hypotenuse means the side which is
exactly opposite to the angle 90 degree
here in the figure AC is the hypotenuse
a
b 90 c

4. A
B C
TO PROVE : We have to prove that퐴퐶2 = 퐴퐵.2 +퐵퐶.2
DATA : In triangle ABC angle ABC =90 degree
CONSTRUCTION : Draw BD perpendicular to AC
D

5. HERE IS THE PROOF
A
D
90
B C
To prove the theorem firstly we have to prove that
Triangles BAD and BDC are similar to triangle ABC
So, at the first we will take the triangle BAD and prove
That it is similar to ABC triangle

6. A
B
D
90
* In triangle ABC and BAD , Angle ABC=BDA=90 DEGREE
BECAUSE , D is perpendicular to AC , So both BDA and BDC=90 DEGREE
• Angle BAC= Angle BAD
because both are common angles or angle comes in both the triangles
* Side BA =BA
Therefore triangle ABC is similar to Triangle BAD
Therefore AC/AB = AB/AD = BC/BD / Because of B.P.T
HERE AC/AB CAME BECAUSE ADB IS 90 DEGREE WHICH IS IN RIGHT AND ABC IS
AT LEFT AC/AB=.SO, AB/BY AD TURNING TRIANGLE 1
BDA TO THE DIRECTION OF ABC , THE B.P.T
IS APPLIED

7. D
B C
*IN triangle ABC and BDC angle ABC=BDC=90 degree
Because AC IS PERPENDICULAR to BD
*Angle BCA and ACD are common angles
*THEREFORE triangle ABC is similar to BDC
Therefore BC/AC = DC/BC 2
90

8. HENCE THE TWO EQUATIONS WHICH WE GOT ARE:
AC/AB = AB/AD
BC/AC = DC/BC
1
2
HENCE ADD THE EQUATIONS:
BY ADDING THEM AND SIMPLIFYING THEM WE GET:
퐴퐶2 = 퐴퐵2 + 퐵퐶2

9. A PRESENTATION FROM
ABHISHEK GANDHI
THANK YOU